Auctions traditionally include the sale of goods from a seller to a buyer. A typical auction includes multiple buyers bidding on a good, referred to as a forward auction. Another type of common auction is a reverse auction or procurement auction, in which multiple sellers compete to sell goods to a single buyer. For example, a procurement auction may include a buyer that needs several lots of several different goods. The buyer receives bids from many sellers for supplying at least a portion of the needed goods at a particular price. Often, the buyer will expend a significant amount of resources, including time, money and other resources, to select a cheapest combination of winning bids to supply all the needed lots of all the goods. Furthermore, a buyer in a procurement auction may have constraints on selecting winning bids. For example, a buyer may want to purchase a certain number of lots from a particular seller or a buyer may want to set a limit on the number of lots that can be purchased from any given seller. Given a large number of bids and constraints, the process of selecting winning bids becomes even more difficult.